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Or bash:
while read L1; do read L2; echo $L1 $L2; done < file
line-01 line-02
line-03 line-04

Or can it be paste?
paste - - < file



--
Note: \t in the replacement part of the "s" command is GNU sed only. For regular sed use actual TAB characters (CTRL-V TAB).

Welcome to the forum.

Does it HAVE to be sed or bash?
awk 'ORS=NR%2?"\t":"\n"' file
line-01 line-02
line-03 line-04


OK, sed is possible, and simple, too:
sed 'N; s/\n/\t/' file...